FINITENESS OF THE LOWER SPECTRUM OF SCHRODINGER-OPERATORS WITH SINGULAR POTENTIALS

We assume that q: R(m) --> R (m greater-than-or-equal-to 3) is a measurable function with the property that its negative and positive parts, respectively, belong to the Kato class K(R(m)) and K(loc)(R(m)). We prove a conjecture by B. Simon concerning the finiteness of the lower spectrum of an s.a. realization of the Schrodinger expression -DELTA + q in L2(R(m)) bounded from below.